I don't know what I did wrong, I showed my work

Can someone please help me with this problem?

Heres the link to the problem:
http://i56.tinypic(dot)com/2822sz7.jpg

^ just change the (dot) to a .

I showed my work on how I got it, but don't quite understand, what I did wrong
This is my work:
http://i51.tinypic(dot)com/a9wyeh.jpg

^change the (dot) to a .

f(x) = 4x² + 12x - 97
      = (4x² + 12x) - 97
      = 4(x² + 3x) - 97
      = 4(x² + 3x + 9/4) - 97 - 9
      = 4(x + 3/2)² - 106 ← you didn't sqrt denominator
vertex = (-3/2, -106)

so
range: {y | y ≥ -106} ← you had the right direction, but dropped the sign

4x² + 12x - 97 = 15
4x² + 12x - 112 = 0
x² + 3x - 28 = 0
(x + 7)(x - 4) = 0
x = -7 and x = 4 ← you dropped the sign again

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